1. **Simplify the fractions $\frac{3}{18}$ and $\frac{18}{45}$.** - To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). - For $\frac{3}{18}$, the GCD of 3 and 18 is 3. $$\frac{3 \div 3}{18 \div 3} = \frac{1}{6}$$ - For $\frac{18}{45}$, the GCD of 18 and 45 is 9. $$\frac{18 \div 9}{45 \div 9} = \frac{2}{5}$$ 2. **Rewrite the fractions $\frac{2}{5}$, $\frac{3}{4}$, and $\frac{2}{3}$ so they all have the same denominator.** - Find the least common denominator (LCD) of 5, 4, and 3. - The LCD is the least common multiple (LCM) of these denominators. - Multiples of 5: 5, 10, 15, 20, 25, 30, ... - Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ... - Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... - The smallest common multiple is 60. - Rewrite each fraction with denominator 60: $$\frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60}$$ $$\frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60}$$ $$\frac{2}{3} = \frac{2 \times 20}{3 \times 20} = \frac{40}{60}$$ **Final answers:** - Simplified fractions: $\frac{1}{6}$ and $\frac{2}{5}$ - Fractions with common denominator 60: $\frac{24}{60}$, $\frac{45}{60}$, and $\frac{40}{60}$